Also he made a highly viral video of him building a minecart rollercoaster during his paid (but cheaper, I believe it was $13, and he was telling people that was half the price that it would be on official release) beta which he got Kotaku and Penny Arcade to share with their massive audience and suddenly he was a millionaire pretty much overnight.
I personally saw the minecart rollercoaster video while browsing Kotaku and that's how I discovered the game.
Notch absolutely marketed and knew how to market his game. He may have not had an advertising budget, but he made the right type of content and the right type of advertising, then shared it with the right types of promotional avenues to reach his target audience to get enough of a start that word-of-mouth advertising could pretty much take over. And that's all marketing really is.
And since then (especially since Microsoft bought Minecraft) you better believe that game has had lots of money dumped into its marketing.
It's just that most things aren't as sexy as a build-your-own-minecart-rollercoaster-brick-by-brick-and-ride-it-in-first-person and therefore require a lot of money to get it in front of enough people.